You may be comfortable graphing the function

f (x) = x²,

but are you equally comfortable graphing these functions,

g(x) = x² + 8,

h (x) = (x-3)² = x² -6x +9?

If you understand graphical transformations, then graphing g (x) and h (x) is no harder than graphing f (x).

Many mathematical models of biological data are based on simple functions whose graphs you know well. However, the actual equations can appear, at first glance, much more complicated. For example,

INSERT EXAMPLE

The following sections will investigate the ways in which we can transform graphs. We group these transformations into:

Throughout these sections we will call the untransformed function the base function and the untransformed graph the base graph.

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In the next section, we will explore vertical translations.

Vertical Translations